The category \(\mathbf {Gr}^{\bullet }\)  is not a category of interest. In [1]} we modified for this category the definition of derived action due to split extensions known for the category of interest [2]} or category of groups with operations [3]}. In analogous way derived action is defined in \(\mathbf {rGr}^{\bullet }\) . This definition derived from split extension agrees with the definition of action in a semi-abelian category [4]}.
